In the motor vehicle manufacture sector, open profiles and profiles welded to one another are increasingly being replaced by thin-walled hollow profiles, the initial form of which is a tube welded along a longitudinal seam. In order to meet the demands of the motor vehicle manufacturing sector for the lowest possible weight and maximum rigidity and strength, the components have on the one hand a particularly low wall thickness and, on the other hand, frequently have a complex shaping. Through the complex shaping, the profiles are adapted exactly to the specific application. In order to economically manufacture hollow profiles or profiles which are formed for specific applications, particularly good monitoring of the manufacturing process is therefore required. The discontinuous mode of work, by forming finished cut-to-size sheets or blanks, has proved its worth in this respect. For example, from the German Patent Specification DE 10 2004 046 687 B3 a method and a device for manufacturing hollow profiles with welded longitudinal seams are known, in which a sheet blank is bent, by relative movements of die halves, freely about a mould core, positioned between the die halves and extending in the longitudinal direction of the sheet blank, the outer form of which mould core determines the inner form of the hollow profile to be manufactured, and the slot profile obtained in this way is then finish-formed over the die halves and the mould core. With this method of manufacture, designated as the rolling-in technique, complex shapings of the hollow profiles can be manufactured only using elaborate mould cores. In particular, the large drawing depths which are frequently needed for complex shaping cannot be achieved by mould cores, or only with difficulty.